In System Settings > Bluetooth, the Bose QC 35 is visible when searching for devices but pairing fails.
After multiple attempts and playing with the PIN options I managed to pair it but once selected in System Settings > Sound, it would fail and fall back to Built-in Audio or playback some garbled sound.
Best Answer
It seems the Bose Quiet Comfort 35 does has issues with pairing with Bluetooth LE (Low Energy).
Get back to a clean state
I would recommend to clean up you past attempts to pair:
Deactivate Bluetooth LE
Edit Bluetooth configuration file:
Replace:
with:
Restart Bluetooth:
Pair
Reactivate Bluetooth LE (optional)
As it is only the pairing that has to be done without Bluetooth LE, once it is paired you can go back to the original configuration:
Replace:
with:
Restart Bluetooth:
Troubleshooting
If you have issues connecting back after disconnecting/rebooting: